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Simplifying (-4 + 6i) + -1(-3 + 12i) = 0 Remove parenthesis around (-4 + 6i) -4 + 6i + -1(-3 + 12i) = 0 -4 + 6i + (-3 * -1 + 12i * -1) = 0 -4 + 6i + (3 + -12i) = 0 Reorder the terms: -4 + 3 + 6i + -12i = 0 Combine like terms: -4 + 3 = -1 -1 + 6i + -12i = 0 Combine like terms: 6i + -12i = -6i -1 + -6i = 0 Solving -1 + -6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -6i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6i = 0 + 1 -6i = 0 + 1 Combine like terms: 0 + 1 = 1 -6i = 1 Divide each side by '-6'. i = -0.1666666667 Simplifying i = -0.1666666667
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